The newborn's name is clearly a nod to her royal heritage, with the infant's middle name a tribute to her great-grandmother the Queen. Other members of the royal family including Zara, Catherine, Duchess of Cambridge, Princess Charlotte, Princess Beatrice and Princess Anne also have Elizabeth as their middle name.
As for her first name, royal reporter Emily Nash tweeted that the couple chose Lena because "it is just a name they liked," according to their spokesperson.
The royal family announced Lena's birth with a statement on their website on June 19.
"Mrs. Michael Tindall was safely delivered of a baby girl on 18th June, at Stroud Maternity Unit. Mr. Tindall was present at the birth. The weight of the baby was 9lbs 3oz," the statement read.
"The Queen, The Duke of Edinburgh, The Princess Royal, Captain Mark Phillips and Mike's parents, Mr Philip and Mrs. Linda Tindall, have been informed and are delighted with the news. The baby's name will be confirmed in due course."
"This baby is the second child for Zara and Mike, the fourth grandchild for The Princess Royal and the seventh great-grandchild for The Queen and The Duke of Edinburgh."
As is the case with many royal babies, the announcement of Lena's name came a few days after her birth, which usually happens for multiple reasons.
"On one hand there's a desire to inform the families before a public declaration is made and any new parent appreciates having a little private time to get to know their new addition before the onslaught of announcements," Victoria Arbiter told Town & Country earlier this year via email.
"Royals, however, also have to consider the great responsibility in naming a new member of the family and I expect they want to be a hundred percent certain of their choice before announcing the name and sealing the baby's place in history."
Lena joins big sister Mia, who was born in 2014.
In December 2016, Zara suffered a miscarriage, with Mike telling The Sunday Times that Mia was a huge blessing to the couple during that time.
"The saving grace for us has been Mia, our daughter who is now 3," he said. "However down we feel she will come running up in our faces. When I was playing I hardly saw her; now we can see her grow up. I can take her swimming and I can take her to Ninja Tots. You'll never be able to see her there because she disappears in a puff of smoke."
Photo Credit: Getty / Max Mumby/Indigo